[DennisP]

You can run that pseudoscience yourself with Zokrates. They have really good documentation, which makes it a lot more concrete. I didn't get zksnarks at all but that cleared it up for me.

https://zokrates.github.io/

The basic idea is that you have functions with both public and private parameters. You can do two things:

1) Pass in all parameters, get back the output and a proof that the output is correct.

2) Pass in just the proof, the output, and the public parameters, and get verification that the function ran correctly; i.e. that the public parameters and some private parameters you don't know generated that output.

So on chain, you can skip storing all the private parameters, as long as you store the proof, and have a contract verify the proof before storing the public data.